Normalization of congruence of bitangents to a hypersurface in \mathbb P³

2021/09/16 by Kim, Hosung, Lee, Yongnam
#14D06 #14J25 (Primary) 14C21 #14M15 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.07655

Abstract

A congruence is a surface in the Grassmannian \rm Gr(2, 4). In this paper, we consider the normalization of congruence of bitangents to a hypersurface in \mathbb P³. We call it the Fano congruence of bitangents. We give a criterion for smoothness of the Fano congruence of bitangents and describe explicitly their degenerations in a general Lefschetz pencil in the space of hypersurfaces in \mathbb P³.

Related

• Secants, bitangents, and their congruences
• Bitangent surfaces and involutions of quartic surfaces
• Moduli of surfaces in ℙ³
• Fano congruences of index 3 and alternating 3-forms
• K-stability and birational models of moduli of quartic K3 surfaces